Modified \(f(R)\)  gravity has also drawn much attention in the last few years. It is based on a generalization of Einstein's field equations by replacing the Ricci scalar curvature, \(R\) , with a general function, \(f(R)\) , in the gravitational action. A relevant feature of \(f(R)\)  gravity is that, differently from \(\Lambda \) CDM standard cosmology based on GR, it is unnecessary postulating dark energy or introduce any kind of new matter field to explain the cosmic inflation [1]}, [2]}, [3]}, [4]} and the present phase of the Universe accelerated expansion [5]}, [6]}. In fact, the simplest \(f(R)\)  model, due to A. Starobinsky [7]}, [8]}, with an additional Ricci scalar quadratic term in the Einstein-Hilbert action and therefore only one free parameter, leads to a de Sitter phase for as long as this term dominates, being compatible with the experimental data collected from the Planck satellite [9]}.
